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Title: Maximum likelihood estimation and the multivariate Bernoulli distribution: An application to reliability

Abstract

We investigate systems designed using redundant component configurations. If external events exist in the working environment that cause two or more components in the system to fail within the same demand period, the designed redundancy in the system can be quickly nullified. In the engineering field, such events are called common cause failures (CCFs), and are primary factors in some risk assessments. If CCFs have positive probability, but are not addressed in the analysis, the assessment may contain a gross overestimation of the system reliability. We apply a discrete, multivariate shock model for a parallel system of two or more components, allowing for positive probability that such external events can occur. The methods derived are motivated by attribute data for emergency diesel generators from various US nuclear power plants. Closed form solutions for maximum likelihood estimators exist in many cases; statistical tests and confidence intervals are discussed for the different test environments considered.

Authors:
Publication Date:
Research Org.:
Los Alamos National Lab., NM (United States)
Sponsoring Org.:
Department of Defense, Washington, DC (United States)
OSTI Identifier:
10171035
Report Number(s):
LA-UR-94-2275; CONF-9406224-1
ON: DE94016070
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: Lifetime data models in reliability and survival,Boston, MA (United States),14-18 Jun 1994; Other Information: PBD: [1994]
Country of Publication:
United States
Language:
English
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NUCLEAR POWER PLANTS; SYSTEM FAILURE ANALYSIS; MAXIMUM-LIKELIHOOD FIT; RELIABILITY; RISK ASSESSMENT; MULTIVARIATE ANALYSIS; 220100; 990200; THEORY AND CALCULATION; MATHEMATICS AND COMPUTERS

Citation Formats

Kvam, P H. Maximum likelihood estimation and the multivariate Bernoulli distribution: An application to reliability. United States: N. p., 1994. Web.
Kvam, P H. Maximum likelihood estimation and the multivariate Bernoulli distribution: An application to reliability. United States.
Kvam, P H. 1994. "Maximum likelihood estimation and the multivariate Bernoulli distribution: An application to reliability". United States. https://www.osti.gov/servlets/purl/10171035.
@article{osti_10171035,
title = {Maximum likelihood estimation and the multivariate Bernoulli distribution: An application to reliability},
author = {Kvam, P H},
abstractNote = {We investigate systems designed using redundant component configurations. If external events exist in the working environment that cause two or more components in the system to fail within the same demand period, the designed redundancy in the system can be quickly nullified. In the engineering field, such events are called common cause failures (CCFs), and are primary factors in some risk assessments. If CCFs have positive probability, but are not addressed in the analysis, the assessment may contain a gross overestimation of the system reliability. We apply a discrete, multivariate shock model for a parallel system of two or more components, allowing for positive probability that such external events can occur. The methods derived are motivated by attribute data for emergency diesel generators from various US nuclear power plants. Closed form solutions for maximum likelihood estimators exist in many cases; statistical tests and confidence intervals are discussed for the different test environments considered.},
doi = {},
url = {https://www.osti.gov/biblio/10171035}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Aug 01 00:00:00 EDT 1994},
month = {Mon Aug 01 00:00:00 EDT 1994}
}

Conference:
Other availability
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